Question
5. What is the next number in this pattern? \[ 0.54,0.6,0.66,0.72, \ldots, \ldots \]
Ask by Stewart Dunn. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The next number in the pattern is 0.78.
Solution
To find the next number in the pattern \(0.54, 0.6, 0.66, 0.72, \ldots\), let's first analyze the differences between the consecutive numbers:
1. The difference between \(0.6\) and \(0.54\) is:
\[
0.6 - 0.54 = 0.06
\]
2. The difference between \(0.66\) and \(0.6\) is:
\[
0.66 - 0.6 = 0.06
\]
3. The difference between \(0.72\) and \(0.66\) is:
\[
0.72 - 0.66 = 0.06
\]
From this, we can see that the pattern increases by \(0.06\) each time.
To find the next number after \(0.72\), we add \(0.06\) to it:
\[
0.72 + 0.06 = 0.78
\]
Thus, the next number in the pattern is \(0.78\).
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Simplify this solution Extra Insights
The pattern in the sequence involves repeatedly adding 0.06 to each number to obtain the next number. After 0.54, we have 0.6 (which is 0.54 + 0.06), then 0.66 (0.6 + 0.06), followed by 0.72 (0.66 + 0.06). Continuing this pattern, we add 0.06 to 0.72, resulting in 0.78. Therefore, the next number in the pattern is 0.78. So the sequence continues with: 0.54, 0.6, 0.66, 0.72, **0.78**.
